I think it's available instantly? A couple of times I've definitely started watching while it's still going on and been able to start from the beginning. The biggest issue is trying to avoid seeing comments/spoilers beforehand!

They're definitely getting quicker but with the downhill there's usually a ten to twenty minute wait between them cutting the live feed and making the recording available. What you don't want to do is watch the live feed at a delay, because the feed cuts no matter how far back you're watching from, generally leaving you with a half hour wait to watch the final 10mins of footage.